= Orthogonalization equation for two statistical parameters
{title2=$\left.\frac{\partial\lambda}{\partial\psi}\right|_\eta=-\frac{I_{\psi\lambda}}{I_{\lambda\lambda}}$}
Write the old <nuisance parameter> as $\lambda=g(\psi,\eta)$ with $g_\eta\ne0$. The transformed <score functions> are $u_\psi^{\rm new}=u_\psi+g_\psi u_\lambda$ and $u_\eta=g_\eta u_\lambda$. Their expected cross product is $g_\eta(I_{\psi\lambda}+g_\psi I_{\lambda\lambda})$. Setting it to zero gives the displayed <ordinary differential equation> along fixed-$\eta$ curves, assuming positive nuisance <Fisher information>. Smooth solutions with distinct initial conditions give a local interest-respecting orthogonal coordinate system.
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